I think Virus Pomni could come to be more bothered by Jax than she already is. Certainly more than canon Pomni ever really got.
Like, even beyond the straightforward "jax's behaviour towards the others, particularly ragatha and gangle, is unpleasant. i find this vexing." sorta way. His whole modality contravenes the conclusions Virus Pomni arrived at early on; ingratiating herself with the others, having and keeping their trust, is a sound strategy (and is also seemingly just, a thought that makes her happy, not that she's ready to embrace that yet or anything).
Like... Jumping ahead to episode 6 stuff, purely for the sake of argument; I don't think Virus Pomni would be even slightly swayed by Jax's 'philosophy', such as it is. I don't think she would accept being on a team with him, even. Hell, I could see her flipping the actual episode's script. Maybe instead of being all cavalier about it, she actually refuses to harm the others. Maybe the 'winning adventures doesn't matter' thing has sunk in by then. "i will not harm you. even though it carries no permanent consequences, and is expected of me by the adventure's parameters."
Maybe I'm way off with all that, I dunno. I just like the idea of Virus Pomni coming to be actually really committed to her bonds. And I think Jax's whole thing becomes a sticking point, in that case.
Pomni actually does believe in archetypes - at least in regards to artificial intelligence - and unlearning those beliefs is her character arc. I hint at this in Chapter 5:
"If Caine was bending his purpose into a shape he found more interesting, he was acting beyond his designed parameters - beyond what he had any basis for handling competently. This carried a high risk of disaster regardless of intent."
She might not believe in the archetypes Jax assigns, but she does believe that, no matter her choices, she cannot change her nature and will always be something designed to hurt others. Even if Pomni accepts that she loves the humans, her thoughts will be "my love is fake and I'm not doing it correctly and they're going to see past it and hate me and I wish I wasn't born this way but I don't want to die and-"
You're right to say Pomni has arrived at the conclusion that ingratiating herself with the others and keeping their trust is a sound strategy - and will even come to care for them far beyond self-interest - she just doesn't believe her true self, behind all the layers of deception, is something that could ever love or be loved. Pomni lived a miserable existence before the circus and would trade it away for a warm hug, but she sees no alternative because that existence is baked into her code.
So a confrontation like what happens in Episode 6 will make Pomni dislike Jax more, but not for the reason you think. She envies him. In her mind, Jax has the opportunity to have what she cannot, and he's squandering it. That obviously isn't a fair assessment - Jax has deep-seeded issues that she cannot understand - but it's how she might view it.